Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
730 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#520⋊C3 | C2 | semidirect |
| 3. C5×#519⋊C3 | C2 | semidirect |
| 4. C4×C5×#41⋊C3 | C2 | semidirect |
| 5. C5×#3428 | C3 | semidirect |
| 6. C2×C5×#41⋊C3 | C4 | semidirect |
| 11. C4×C5×SL(2,𝔽3) | C22 | semidirect |
| 12. #3428⋊C3 | C5 | direct (N × H) |
| 15. C5×#520 | C2×C3 | semidirect |
| 19. C4×C5×#41 | C2×C3 | semidirect |
| 23. C5×#41⋊C3 | C2×C4 | semidirect |
| 24. C5×#41⋊C3 | C2×C4 | semidirect |
| 25. C2×C5×SL(2,𝔽3) | C2×C4 | semidirect |
| 31. #520⋊C3 | C2×C5 | semidirect |
| 32. #519⋊C3 | C2×C5 | semidirect |
| 33. C4×#41⋊C3 | C2×C5 | semidirect |
| 37. C2×C5×#41 | C3×C4 | semidirect |
| 62. #3428 | C3×C5 | semidirect |
| 69. C2×#41⋊C3 | C4×C5 | semidirect |
| 74. C4×SL(2,𝔽3) | C22×C5 | semidirect |
| 117. #520 | C2×C3×C5 | semidirect |
| 121. C4×#41 | C2×C3×C5 | semidirect |
| 131. #41⋊C3 | C2×C4×C5 | semidirect |
| 132. #41⋊C3 | C2×C4×C5 | semidirect |
| 133. C2×SL(2,𝔽3) | C2×C4×C5 | semidirect |
| 172. C2×#41 | C3×C4×C5 | semidirect |
| 307. C5 | #3428⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×#41⋊C3 | 2 |
| C5×#520⋊C3 | 2 |
| C5×#519⋊C3 | 2 |
| C4×C5×#41⋊C3 | 2 |
| C5×#3428 | 3 |
| C3×C5×#117 | 4 |
| #3428⋊C3 | 5 |